KMoffett has already said it is corrosion free.is this circuit corrosion free if yes then please explain how it is using DC POWER SUPPLY.
The probes are connected via C2 and C3 to the rest of the circuit. DC is blocked by those capacitors and as the oscillator output voltage rises and falls the capacitors couple an alternating voltage to the probes. The period that either probe is positive is approximately equal to the period that it is negative, so there is negligible net DC, thus preventing corrosion.
1) Have you provided a true earth connection (e.g. to a water pipe) to the circuit as I suggested?
2) Having properly earthed the circuit does the LED still come on with one probe immersed, when you are nowhere near the circuit? If so, is it the probe connected to C2 or the one connected to C3?
3) Why are you "moving this circuit in the air"? Keep it still.
4) Don't use long wires (which act as antennas) to connect to your circuit.
5) Use a battery to power the circuit; not a mains-powered supply.